J. Oksman Department of Electrical Engineering, university of Oulu, Finland E. Kataja Geophysical Observatory, Sodank,ylt?. Finhnd

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1 Geophys. J. R. astr. SOC. (1981) 65, IMF polarity and annual variations of the Dst index J. Oksman Department of Electrical Engineering, university of Oulu, Finland E. Kataja Geophysical Observatory, Sodank,ylt?. Finhnd Received 1980 August 15; in original form 1980 June 24 Summary. The annual variations of the Dst index were studied separately for the towards and away polarities of the interplanetary magnetic field. It was found that: (a) the towards polarity is associated with a spring minimum and the away polarity with an autumn minimum of Dst; (b) that both polarities exhibit an asymmetry between the solstices, the Dst values for the December solstice being more negative than those for the June solstice; and (c) that a shift of the annual minima in Dst to earlier times with increasing level of activity seems to exist, irrespective of IMF polarity. The first effect is related to the similar effect found earlier in other measures of geomagnetic activity and is assumed to be caused by varying energy transfer from the solar wind into the magnetosphere depending on the sign of the north-south component of the IMF; the second effect is compatible with a proposed annual variation in the size of the magnetosphere, the reason of which is still unknown; and the third suggests to us that the solar magnetospheric coordinate system might not be adequate for describing the interaction between the IMF and the magnetosphere during disturbed times. Introduction In his study on the annual variations of the Dst index, related to the strength of the ring current surrounding the Earth, Mayaud (1978) found, using harmonic analysis, a 6- wave and a 12- wave. He attributed both waves to the variation of the mean latitude of the ring current in the course of the year, proposed by Malin & Isikara (1976), and to the northern latitude of most of the Dst observatories. Since the pioneering work of Russell & McPherron (1973) it is known that the geomagnetic activity is modulated by the polarity of the interplanetary magnetic field (IMF). As the ring current is enhanced during magnetic storms, it can be expected that a corresponding modulation in the mean intensity of the ring current (and hence in the average Dst index) should be discernible. The purpose of this report is to show that this really is the case and that most of the 6- wave probably is caused by this modulation. An alternative

2 604 J. Oksman and E. Kataja explanation is also suggested for the 12- wave, based on the fact that the Dst field is partly due to surface currents at the magnetopause. Annual variations of the Dst index The daily mean values of the Dst index, taken from IACA Bulletins for the years , well covering the sunspot cycle 20, were used in this study. As a first step, the mean annual variation of all values of Dst (irrespective of IMF polarity) was determined by forming the medians and quartiles of the ly means for each of the year (Fig. 1). The quartiles were formed for two reasons: (1) they give a measure for the spread because they border half of the of the data points, and (2) they yield the possibility of examining quiet and disturbed periods (I and 111 quartile, respectively) separately. Two waves are obvious in the median, namely, (1) a clear semi-annual (6-) wave with minima at equinoxes and a double amplitude of about lont, and (2) an annual (12- ) wave with lower values near the December than the June solstice and with a double amplitude of about 5 nt. 0 J F M A M J J A S O N O Figure 1. Annual variation of the ly medians (solid line) and quartiles (dotted lines) of Dst in AU values in one group. In spite of the relatively large spread (difference of the quartiles varies from 10 to 15 nt), both waves are seen also in the quartiles, although the amplitudes are smaller in the I quartile which corresponds to more quiet periods. It is also interesting to note that the minima of the 111 quartile, which corresponds to more disturbed times, tend to occur earlier than those of the median and the I quartile. Next, the Dst values were subdivided into two groups according to IMF polarity on the day in question. These polarities were taken from tables published by NOAA in Solar Geophysical Data. The determination of IMF polarity, used by NOAA, is based on the fact that the diurnal variations of the geomagnetic field at polar cap stations. Thuie and Vostok depend on the sign of the azimuthal component of the IMF (By). The radial component of the IMF (B,) can in statistical studies be assumed to have the opposite sign to By because exceptions from this rule are rare (Friis-Christensen et al. 1972). We have, therefore, assumed the cases with positive By to correspond to the away (A) polarity and those with negative By to the towards (T) polarity of the IMF. The mean values of Dst were calculated for each of each year for the two polarities separately, and then the medians and quartiles of these ly means were

3 IMF polarity and the Dst index 605 D J F M A M J J A S O N D 101 I I I,, I 1 I I 1 1 I D J F M A M J J A S O N D I 1 I I I I 1 I Figure 2. Annual variations of the ly medians (solid lines) and quartiles (dotted lines) of Dst in The values were grouped according to IMF polarity. (a) T polarity, (b) A polarity. determined. The results are shown in Fig. 2(a) for the T polarity and in Fig. 2(b) for the A polarity. The following features can be seen: (1) A spring minimum of Dst seems to be associated with the T polarity and an autumn minimum with the A polarity of the IMF. (2) The minimum in Fig. 2(a) is rounded whereas that in Fig. 2(b) is peaked. (3) The annual wave, i.e. the differences between the solstices discussed above, exists for both polarities. (4) A small secondary minimum exists in both figures, namely in the autumn for the T polarity and (barely visibly) in the spring for the A polarity. (5) As in Fig. 1, the minima of the 111 quartile tend to occur earlier than those of the median or the I quartile (especially clear for the A polarity). In Fig. 3 the medians and quartiles of the difference between the ly means for the two polarities (A-T) are shown. We get the following results: (1) A-T exhibits a clear annual wave with a spring maximum and an autumn minimum and a double amplitude of about 15 nt. (2) Corresponding to the difference in shape of the minima in Fig. 2 (a and b) the halfwaves have different shapes, the spring half being rounded and the autumn half peaked. (3) As could be expected, the difference between the solstices has been cancelled out in A-T. Discussion The polarity effect shown in Fig. 2 (a and b) (and Fig. 3) seems to be another indication of the modulation of energy input from the solar wind into the magnetosphere by the IMF. When the north-south component of the IMF (Bz) in the solar magnetospheric coordinate

4 606 J. Oksman and E. Kataja O J F M A M J J A S O N D 201 I I I I I, I I I I Figure3. Annual variation of the ly medians (solid line) and quartiles (dotted lines) of the difference A-T in system is negative, energy is transferred much more effectively from the solar wind into the magnetosphere than when it is positive (Russell & McPherron 1973; Siscoe & Crooker 1974; Burton, McPherron & Russell 1975a). The difference in the annual variations for the two polarities is caused by the fact that B, has, due to the changing inclination of the geomagnetic axis in the course of the year, on the average, highest negative values for the T polarity in the spring and for the A polarity in the autumn (Russell & McPherron 1973). The corresponding IMF polarity effect has been discovered earlier in other indices of geomagnetic activity: in C9 (Russell & McPherron 1973), in AU and AL (Burch 1973), in Kp (Murayama 1974; McDiamid & Budzinski 1975), as well as in Am and AE (Berthelier 1976). As to Dst, Kane (1974) found that turning ofb, from a northward (positive) to a southward (negative) direction triggers a build-up of the ring current a few hours later, and Burton, McPherron & Russell (1975b) formulated an empirical relationship between Dst and the north-south component of the IMF. As far as we are aware, the polarity effect in the annual variations of Dst has not been presented earlier. The difference in the shapes of the annual variations for the two polarities in Fig. 2 might be due to statistical fluctuations. If it is real, the model for interaction of the magnetic fields used here has to be modified to account for it. It is possible that the secondary minima in Fig. 2 (a and b), pointed out before, are due to the fact that the derived IMF polarity might in some cases be incorrect. It has been shown by Russell, Burton & McPherron (1975) and Berthelier & Gukrin (1975) that the polarity determination from the polar cap magnetograms is in some cases, especially on disturbed days, problematic and can lead to a wrong polarity. We think that the secondary minimum in the autumn in Fig. 2(a) is caused by the fact that a relatively small number of A days has been assigned with the T polarity. This assumption is supported by the fact that the secondary minimum is deepest in the I11 quartile which corresponds to disturbed times. The very shallow secondary minimum in the spring in Fig. 2(b) suggests that the opposite error is less frequent. The 12- wave present in Figs 1 and 2 is very interesting. Mayaud (1978) suggests that the annual wave can be explained by the mechanism proposed by Malin & Isikara (1976): the mean latitude of the ring current is assumed to move, due to the distortion of the magnetosphere caused by the solar wind, north at the December solstice and south at the June solstice. This movement would result in more negative values of Dst near the December solstice because most of the geomagnetic stations used for Dst determination are located in the northern hemisphere. Malin & Isikara proposed their mechanism for the explanation of the g! coefficient in the

5 IMF polarity and the Dst index 607 spherical harmonic presentation of the geomagnetic field, describing the annual variation in the difference of the geomagnetic field in the two hemispheres (smaller values in local winter than in local summer). In addition to this term, Malin & Isikara found an appreciable coefficient g! describing the annual change in the global magnetic field (the field is several nt smaller in December than in June); this change is similar in phase and magnitude to the annual variation present in Figs 1 and 2 and also in Mayaud s results. The Malin & Isikara mechanism could possibly, at least qualitatively, explain an annual variation in Dst but it cannot be responsible for the annual wave in the global field. Malin & Isikara offer no other explanation for g! than an enhancement and diminution (for some unknown reason) of the mean ring current in the course of the year. We suggest the following mechanism to account for the annual variation of the global field and for the most part of the annual wave in Dst. The Dst index (Sugiura 1964) expresses the disturbance in the horizontal component of the geomagnetic field near the equator. It is defined as the combined field of the ring current, the tail current and the magnetospheric boundary current. The boundary current enhances the Earth s main field, and this enhancement depends on the size of the magnetosphere (smaller size corresponding to a larger enhancement), whereas the ring current and tail current reduce it (Su & Konradi 1975). Because the influence of the tail current is small, Dst is, in effect, determined by a balance between the ring current and the boundary current. It seems possible to us that the average value of the ring current field is not appreciably different in June and December. A check made by us using the geomagnetic activity index aam of Mayaud revealed the same mean activity level in June and December, suggesting that the annual wave in the ring current (which has a good correlation with geomagnetic activity) might be negligible. The observed solsticial difference in Dst would then be caused by different values of the boundary current field: a more negative value of Dst would correspond to a smaller boundary current field and this, in turn, to a larger magnetosphere. The magnetosphere would, according to this reasoning, be larger in December than in June. A variation in this sense was suggested several years ago by Oksman (1971), basing on indirect evidence. No explanation has so far been found for this proposed variation. From the empirical relation between the stand-off distance and Dst, derived by Su & Konradi (1975), it can be estimated that an annual variation by less than one Earth s radius in the stand-off distance would explain the observed annual wave in Dst. It is interesting to note that Siscoe (1979) connects high negative values of Dst with large magnetospheric size by a different way of reasoning. In the outer part of the magnetosphere the ring current field increases the main geomagnetic field. An intensified ring current, causing high negative Dst values on ground, thus means that the solar wind encounters an enhanced geomagnetic field, leading to an increased stand-off distance and a larger magnetosphere. The finding that the disturbance in the Dst field tends to shift to earlier times with increasing level of disturbance agrees with the result presented by Chapman & Bartels (1940) concerning their activity index ul, an older measure for the disturbance of the horizontal component near the equator: They found u1 to maximize in April and October in years of low activity with a tendency for the maxima to shift towards March and September with increasing activity. We propose the following tentative explanation for this effect. If the energy transfer from the solar wind into the magnetosphere were modulated by the z-component of the IMF in the geocentric solar magnetospheric coordinate system, where the z-axis is perpendicular to the Sun-Earth line and lies in the plane determined by this line

6 608 J. Oksman and E. Kataja and the geomagnetic axis (Russell 1971), the maxima of geometric activity would occur near April 5 and October 5 (Russell & McPherron 1973). If, on the other hand, the z-component of the IMF, responsible for the modulation of the geomagnetic activity, were to be taken in the solar magnetic coordinate system, where the z-axis is parallel to the geomagnetic axis (Russell 1971), the annual maxima in geomagnetic activity would occur earlier than above: the normal azimuth angles 45" and 335" would correspond to maxima of geomagnetic activity on August 15 and February 15 (Russell & McPherron 1973). We propose that the solar magnetospheric coordinate system is a good frame of reference for studying the interaction between the IMF and the geomagnetic field during weak and moderate geomagnetic activity (when the solar wind is weak and the magnetosphere large) but that the actual direction of the geomagnetic axis has a stronger influence on the interaction during strong activity (when the solar wind exerts a stronger pressure and the magnetosphere is smaller), leading to a shift of the annual maxima of activity to earlier times. Acknowledgments We are grateful to Professor E. -A. Lauter of the Central Institute of Solar-Terrestrial Physics, Academy of Sciences of the GDR, for suggesting this topic to us. References Berthelier, A., Influence of the polarity of the interplanetary magnetic field on the annual and the diurnal variations of magnetic activity, J. geophys. Res., 81, Berthelier, A. & Gukrin, C., Comment on 'Interplanetary Magnetic Sector Structure, ' by L. Svalgaard, J. geophys. Res., 80, Burch, J. L., Effects of interplanetary magnetic sector structure on auroral zone and polar cap magnetic activity, J. geophys. Res., 78, Burton, R. K., McPherron, R. L. & Russell, C. T., 1975a. The terrestrial magnetosphere: a half-wave rectifier of the interplanetary electric field, Science, 189, Burton, R. K., McPherson, R. L. & Russell, C. T., 1975b. An empirical relationship between interplanetary conditions and Dst, J. geophys. Res., 80, Chapman, S. & Bartels. J., Geomugnetism, p. 366, Clarendon Press, Oxford. Friis-Christensen, E., Lassen, K., Wilhjelm, J. M., Gonzales, W. & Colburn, D. S., Critical component of the interplanetary magnetic field responsible for large geomagnetic effects in the polar cap, J. geophys. Res., 77, Kane, R. P., Relationship between interplanetary plasma parameters and geomagnetic Dst, J. geophys. Res., 79, McDiarmid, I. B. & Budzinski, E. E., Kp dependence on sectors, J. geophys. Res., 80, Malin, S. R. C. & Isikara, A. M., Annual variation of the geomagnetic field, Geophys. J. R. ustr. SOC., 47, Mayaud, P. N., The annual and daily variations of the Dst index, Geophys. J. R. ustr. Soc., 55, Murayama, T., Origin of the semiannual variation of geomagnetic Kp indices, J. geophys. Res., 79, Oksman, J., Proposed annual and sunspot cycle variation of the plasmasphere of the Earth, Nature, 231, Russell, C. T., Geophysical coordinate transformations, Cosm. Electr. 2, Russell, C. T., Burton, R. K. & McPherron, R. L., Some properties of the Svalgaard A/C index, J. geophys Res., 80, Russell, C. T. & McPherron, R. L., Semiannual variation of geomagnetic activity,j. geophys. Res., 78,

7 IMF polarity and the Dst index 609 Siscoe, G. L., A Dst contribution to the equatorward shift of the aurora, Planet. Space Sci., 27, Siscoe, G. L. & Crooker, N., A theoretical relation between Dst and the solar wind merging electric field, Geophys. Res. Left., 1, Su, S. -Y.& Konradi, A., Magnetic field depression at the Earth s surface calculated from the relationship between the size of the magnetosphere and the Dst values, J. geophys. Res. 80, Sugiura, M., Hourly values of equatorial Dst for the ICY, Ann. Int. geophys. Year, 35,9-45.